Asymptotic Issues For Some Partial Differential Equations PDF Download
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Author | : Michel Marie Chipot |
Publisher | : World Scientific |
Total Pages | : 283 |
Release | : 2024-04-15 |
Genre | : Mathematics |
ISBN | : 9811290458 |
Download Asymptotic Issues For Some Partial Differential Equations (Second Edition) Book in PDF, ePub and Kindle
The primary focus of the book is to explore the asymptotic behavior of problems formulated within cylindrical structures. Various physical applications are discussed, with certain topics such as fluid flows in channels being particularly noteworthy. Additionally, the book delves into the relevance of elasticity in the context of cylindrical bodies.In specific scenarios where the size of the cylinder becomes exceptionally large, the material's behavior is determined solely by its cross-section. The investigation centers around understanding these particular properties.Since the publication of the first edition, several significant advancements have been made, adding depth and interest to the content. Consequently, new sections have been incorporated into the existing edition, complemented by a comprehensive list of references.
Author | : Michel Chipot |
Publisher | : |
Total Pages | : 252 |
Release | : 2016 |
Genre | : MATHEMATICS |
ISBN | : 9781783268924 |
Download Asymptotic Issues for Some Partial Differential Equations Book in PDF, ePub and Kindle
Author | : O. A. Oleĭnik |
Publisher | : Cambridge University Press |
Total Pages | : 218 |
Release | : 1996-03-21 |
Genre | : Mathematics |
ISBN | : 9780521485371 |
Download Some Asymptotic Problems in the Theory of Partial Differential Equations Book in PDF, ePub and Kindle
In 1993, Professor Oleinik was invited to give a series of lectures about her work in the area of partial differential equations. This book contains those lectures, and more.
Author | : M.V. Fedoryuk |
Publisher | : Springer Science & Business Media |
Total Pages | : 248 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642584233 |
Download Partial Differential Equations V Book in PDF, ePub and Kindle
In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution.
Author | : Joseph B. Keller |
Publisher | : Springer |
Total Pages | : 273 |
Release | : 2013-12-21 |
Genre | : Mathematics |
ISBN | : 1489904360 |
Download Surveys in Applied Mathematics Book in PDF, ePub and Kindle
Partial differential equations play a central role in many branches of science and engineering. Therefore it is important to solve problems involving them. One aspect of solving a partial differential equation problem is to show that it is well-posed, i. e. , that it has one and only one solution, and that the solution depends continuously on the data of the problem. Another aspect is to obtain detailed quantitative information about the solution. The traditional method for doing this was to find a representation of the solution as a series or integral of known special functions, and then to evaluate the series or integral by numerical or by asymptotic methods. The shortcoming of this method is that there are relatively few problems for which such representations can be found. Consequently, the traditional method has been replaced by methods for direct solution of problems either numerically or asymptotically. This article is devoted to a particular method, called the "ray method," for the asymptotic solution of problems for linear partial differential equations governing wave propagation. These equations involve a parameter, such as the wavelength. . \, which is small compared to all other lengths in the problem. The ray method is used to construct an asymptotic expansion of the solution which is valid near . . \ = 0, or equivalently for k = 21r I A near infinity.
Author | : H.G. Kaper |
Publisher | : Springer Science & Business Media |
Total Pages | : 371 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401118108 |
Download Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters Book in PDF, ePub and Kindle
This volume contains the proceedings of the NATO Advanced Research Workshop on "Asymptotic-induced Numerical Methods for Partial Differ ential Equations, Critical Parameters, and Domain Decomposition," held at Beaune (France), May 25-28, 1992. The purpose of the workshop was to stimulate the integration of asymp totic analysis, domain decomposition methods, and symbolic manipulation tools for the numerical solution of partial differential equations (PDEs) with critical parameters. A workshop on the same topic was held at Argonne Na tional Laboratory in February 1990. (The proceedings were published under the title Asymptotic Analysis and the Numerical Solu.tion of Partial Differ ential Equations, Hans G. Kaper and Marc Garbey, eds., Lecture Notes in Pure and Applied Mathematics. Vol. 130, ·Marcel Dekker, Inc., New York, 1991.) In a sense, the present proceedings represent a progress report on the topic area. Comparing the two sets of proceedings, we see an increase in the quantity as well as the quality of the contributions. 110re research is being done in the topic area, and the interest covers serious, nontrivial problems. We are pleased with this outcome and expect to see even more advances in the next few years as the field progresses.
Author | : Hans G. Kaper |
Publisher | : CRC Press |
Total Pages | : 290 |
Release | : 1991-02-25 |
Genre | : Mathematics |
ISBN | : 9780585319674 |
Download Asymptotic Analysis and the Numerical Solution of Partial Differential Equations Book in PDF, ePub and Kindle
Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per
Author | : Kelei Wang |
Publisher | : Springer Science & Business Media |
Total Pages | : 117 |
Release | : 2014-07-08 |
Genre | : Mathematics |
ISBN | : 3642336965 |
Download Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations Book in PDF, ePub and Kindle
This thesis is devoted to the study of the asymptotic behavior of singularly perturbed partial differential equations and some related free boundary problems arising from these two problems. We study the free boundary problems in the singulary limit and give some characterizations, and use this to study the dynamical behavior of competing species when the competition is strong. These results have many applications in physics and biology.
Author | : Dmitrii Korikov |
Publisher | : Springer Nature |
Total Pages | : 404 |
Release | : 2021-04-01 |
Genre | : Mathematics |
ISBN | : 3030653722 |
Download Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains Book in PDF, ePub and Kindle
This book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on. In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary. The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods.
Author | : Lamberto Cesari |
Publisher | : Springer |
Total Pages | : 278 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662015293 |
Download Asymptotic Behavior and Stability Problems in Ordinary Differential Equations Book in PDF, ePub and Kindle
In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepen ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, auto matic controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call "qualitative theory of differential equations". The purpose of the present volume is to present many of the view points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications.